I am teaching my son the multiplication tables in a Trachtenberg kind of way.

The tables until 6 are easy for him. We are now training to do 8-12.

7 is the most difficult for him (as it is for many kids).

We have already done ‘sequences’ for about two years. I started doing those from when they were 3-4 years old.

A sequence is 2, 4, 6, 8, …

Or 3, 6, 9, 12, …

Or 7, 14, 21,…

etc.

My youngest is 5 and with her I only do the sequences.

My oldest is now learning the tables at school.

What I do for numbers close to 10 (8 - 12) is this.

I have him first add a zero to the number (multiplication by 10) and then add or subtract the number or twice the number.

11 = 10 + 1, so:

1 * 11 = 10 + 1 = 11

2 * 11 = 20 + 2 = 22

3 * 11 = 30 + 3 = 33

4 * 11 = 40 + 4 = 44

5 * 11 = 50 + 5 = 55

6 * 11 = 60 + 6 = 66

7 * 11 = 70 + 7 = 77

8 * 11 = 80 + 8 = 88

9 * 11 = 90 + 9 = 99

10 * 11 = 100 + 10 = 110

11 * 11 = 110 + 11 = 121

12 * 11 = 120 + 12 = 132

9 = 10 - 1, so:

1 * 9 = 10 - 1 = 9

2 * 9 = 20 - 2 = 18

3 * 9 = 30 - 3 = 27

4 * 9 = 40 - 4 = 36

5 * 9 = 50 - 5 = 45

6 * 9 = 60 - 6 = 54

7 * 9 = 70 - 7 = 63

8 * 9 = 80 - 8 = 72

9 * 9 = 90 - 9 = 81

10 * 9 = 100 - 10 = 90

11 * 9 = 110 - 11 = 99

12 * 9 = 120 - 12 = 108

12 = 10 + 2, so:

1 * 12 = 10 + 2 = 12

2 * 12 = 20 + 4 = 24

3 * 12 = 30 + 6 = 36

4 * 12 = 40 + 8 = 48

5 * 12 = 50 + 10 = 60

6 * 12 = 60 + 12 = 72

7 * 12 = 70 + 14 = 84

8 * 12 = 80 + 16 = 96

9 * 12 = 90 + 18 = 108

10 * 12 = 100 + 20 = 120

11 * 12 = 110 + 22 = 132

12 * 12 = 120 + 24 = 144

8 = 10 - 2, so:

1 * 8 = 10 - 2 = 8

2 * 8 = 20 - 4 = 16

3 * 8 = 30 - 6 = 24

4 * 8 = 40 - 8 = 32

5 * 8 = 50 - 10 = 40

6 * 8 = 60 - 12 = 48

7 * 8 = 70 - 14 = 56

8 * 8 = 80 - 16 = 64

9 * 8 = 90 - 18 = 72

10 * 8 = 100 - 20 = 80

11 * 8 = 110 - 22 = 88

12 * 8 = 120 - 24 = 96

We have not yet done a lot with the 7 table.

We do the 7 sequence from time to time.

For the table I plan to use the following.

He is quick to halve.

7 is 5 + 2. 5 is halve of ten and 2 is double of one.

So I call it ’ halve and double’. There is a shift between halve and double, but ‘halve and double’ just sounds better.

In the case of 4 (times 7), we do halve of 4 (2) and double 4 (8).

I have him picture the 2 next to the 8 to form 28.

In the case of 8, again we do halve of 8 (4) and double (16).

He knows by then he needs to concatenate them, effectively picturing 4|16 = 56. Or he can just do 40+16.

Btw, I don’t force him to do anything. I just show him options.

Until now he just picks them up easily.

For even numbers ‘halve plus double’ is easy:

2 * 7 = 1|4 = 14

4 * 7 = 2|8 = 28

6 * 7 = 3|12 = 42

8 * 7 = 4|16 = 56

10 * 7 = 5|20 = 70

12 * 7 = 6|24 = 84

For odd numbers I just have him get the next number in the sequence.

Either that or have him multiply the number by 10, halve and then double:

1 * 7 = 5 + 2 = 7

2 * 7 = 10 + 4 = 14

3 * 7 = 15 + 6 = 21

4 * 7 = 20 + 8 = 28

5 * 7 = 25 + 10 = 35

6 * 7 = 30 + 12 = 42

7 * 7 = 35 + 14 = 49

8 * 7 = 40 + 16 = 56

9 * 7 = 45 + 18 = 63

10 * 7 = 50 + 20 = 70

11 * 7 = 55 + 22 = 77

12 * 7 = 60 + 24 = 84